TSTP Solution File: GRP229-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP229-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:46:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP229-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 06:37:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 484 clauses, backtracked 251 clauses, performed 12 splits and kept 456 clauses.
% 0.19/0.43 SPASS allocated 63449 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.03 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.03 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 5, length 274 :
% 0.19/0.43 % SZS output start Refutation
% 0.19/0.43 1[0:Inp] || -> equal(inverse(sk_c8),sk_c7)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.43 2[0:Inp] || -> equal(inverse(sk_c4),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.43 3[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.43 4[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.43 5[0:Inp] || -> equal(inverse(sk_c1),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.43 6[0:Inp] || -> equal(inverse(sk_c5),sk_c8)** equal(inverse(sk_c1),sk_c8).
% 0.19/0.43 7[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.43 8[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.43 9[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.19/0.43 11[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6)** equal(multiply(sk_c1,sk_c7),sk_c8).
% 0.19/0.43 12[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.43 13[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 14[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 15[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 16[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 17[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 18[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 19[0:Inp] || -> equal(inverse(sk_c8),sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 20[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 21[0:Inp] || -> equal(multiply(sk_c4,sk_c7),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 22[0:Inp] || -> equal(multiply(sk_c8,sk_c6),sk_c7)** equal(multiply(sk_c2,sk_c8),sk_c3).
% 0.19/0.43 23[0:Inp] || -> equal(multiply(sk_c5,sk_c8),sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 24[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 25[0:Inp] || -> equal(inverse(sk_c8),sk_c7)** equal(inverse(sk_c2),sk_c8).
% 0.19/0.43 26[0:Inp] || -> equal(inverse(sk_c4),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.43 27[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.43 28[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.43 29[0:Inp] || -> equal(inverse(sk_c2),sk_c8) equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.43 30[0:Inp] || -> equal(inverse(sk_c5),sk_c8) equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.43 31[0:Inp] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** equal(multiply(sk_c8,v),sk_c7)** equal(multiply(w,sk_c8),v)* equal(inverse(w),sk_c8) equal(inverse(sk_c8),sk_c7) equal(inverse(x),sk_c8) equal(multiply(x,sk_c7),sk_c8)** equal(multiply(sk_c8,y),sk_c7)** equal(multiply(z,sk_c8),y)* equal(inverse(z),sk_c8) -> .
% 0.19/0.43 32[0:Inp] || -> equal(multiply(identity,u),u)**.
% 0.19/0.43 33[0:Inp] || -> equal(multiply(inverse(u),u),identity)**.
% 0.19/0.43 34[0:Inp] || -> equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w)))**.
% 0.19/0.43 35[0:Con:31.6] || equal(inverse(u),sk_c8) equal(inverse(v),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),w)*+ equal(multiply(v,sk_c7),sk_c8)** equal(multiply(sk_c8,w),sk_c7)** -> .
% 0.19/0.43 36[1:Spt:35.1,35.4] || equal(inverse(u),sk_c8) equal(multiply(u,sk_c7),sk_c8)** -> .
% 0.19/0.43 39[2:Spt:1.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.43 47[3:Spt:7.1] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.43 49[3:SpL:47.0,36.1] || equal(inverse(sk_c1),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.19/0.43 50[3:Obv:49.1] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.43 51[3:Rew:39.0,50.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.43 52[3:Obv:51.0] || -> .
% 0.19/0.43 53[3:Spt:52.0,7.1,47.0] || equal(multiply(sk_c1,sk_c7),sk_c8)** -> .
% 0.19/0.43 54[3:Spt:52.0,7.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.43 56[3:MRR:8.1,53.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.43 59[3:MRR:9.1,53.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.43 66[3:SpL:59.0,36.1] || equal(inverse(sk_c4),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.19/0.43 67[3:Obv:66.1] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.43 68[3:Rew:56.0,67.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.43 69[3:Obv:68.0] || -> .
% 0.19/0.43 70[2:Spt:69.0,1.1,39.0] || equal(inverse(sk_c1),sk_c8)** -> .
% 0.19/0.43 71[2:Spt:69.0,1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.43 73[2:MRR:2.1,70.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.43 76[2:MRR:3.0,70.0] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.43 83[2:SpL:76.0,36.1] || equal(inverse(sk_c4),sk_c8)** equal(sk_c8,sk_c8) -> .
% 0.19/0.43 84[2:Obv:83.1] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.43 85[2:Rew:73.0,84.0] || equal(sk_c8,sk_c8)* -> .
% 0.19/0.43 86[2:Obv:85.0] || -> .
% 0.19/0.43 87[1:Spt:86.0,35.0,35.2,35.3,35.5] || equal(inverse(u),sk_c8) equal(inverse(sk_c8),sk_c7) equal(multiply(u,sk_c8),v)*+ equal(multiply(sk_c8,v),sk_c7)** -> .
% 0.19/0.43 89[1:SpL:32.0,87.2] || equal(inverse(identity),sk_c8) equal(inverse(sk_c8),sk_c7) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.43 90[2:Spt:1.0] || -> equal(inverse(sk_c8),sk_c7)**.
% 0.19/0.43 92[2:Rew:90.0,89.1] || equal(inverse(identity),sk_c8) equal(sk_c7,sk_c7) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.43 95[2:Obv:92.1] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.43 98[3:Spt:6.0] || -> equal(inverse(sk_c5),sk_c8)**.
% 0.19/0.43 100[4:Spt:2.0] || -> equal(inverse(sk_c4),sk_c8)**.
% 0.19/0.43 102[5:Spt:5.1] || -> equal(multiply(sk_c5,sk_c8),sk_c6)**.
% 0.19/0.43 105[2:SpR:90.0,33.0] || -> equal(multiply(sk_c7,sk_c8),identity)**.
% 0.19/0.43 106[3:SpR:98.0,33.0] || -> equal(multiply(sk_c8,sk_c5),identity)**.
% 0.19/0.43 107[4:SpR:100.0,33.0] || -> equal(multiply(sk_c8,sk_c4),identity)**.
% 0.19/0.43 108[6:Spt:4.1] || -> equal(multiply(sk_c8,sk_c6),sk_c7)**.
% 0.19/0.43 110[7:Spt:3.1] || -> equal(multiply(sk_c4,sk_c7),sk_c8)**.
% 0.19/0.43 116[0:SpR:33.0,34.0] || -> equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v))**.
% 0.19/0.43 118[2:SpR:105.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),multiply(identity,u))**.
% 0.19/0.43 119[6:SpR:108.0,34.0] || -> equal(multiply(sk_c8,multiply(sk_c6,u)),multiply(sk_c7,u))**.
% 0.19/0.43 121[2:Rew:32.0,118.0] || -> equal(multiply(sk_c7,multiply(sk_c8,u)),u)**.
% 0.19/0.43 122[0:Rew:32.0,116.0] || -> equal(multiply(inverse(u),multiply(u,v)),v)**.
% 0.19/0.43 132[6:SpR:108.0,121.0] || -> equal(multiply(sk_c7,sk_c7),sk_c6)**.
% 0.19/0.43 133[3:SpR:106.0,121.0] || -> equal(multiply(sk_c7,identity),sk_c5)**.
% 0.19/0.43 134[4:SpR:107.0,121.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.19/0.43 135[4:Rew:133.0,134.0] || -> equal(sk_c5,sk_c4)**.
% 0.19/0.43 137[5:Rew:135.0,102.0] || -> equal(multiply(sk_c4,sk_c8),sk_c6)**.
% 0.19/0.43 141[4:Rew:135.0,133.0] || -> equal(multiply(sk_c7,identity),sk_c4)**.
% 0.19/0.43 146[6:SpR:132.0,34.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),multiply(sk_c6,u))**.
% 0.19/0.43 148[4:SpR:141.0,34.0] || -> equal(multiply(sk_c7,multiply(identity,u)),multiply(sk_c4,u))**.
% 0.19/0.43 150[4:Rew:32.0,148.0] || -> equal(multiply(sk_c4,u),multiply(sk_c7,u))**.
% 0.19/0.43 151[5:Rew:150.0,137.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.43 152[7:Rew:150.0,110.0] || -> equal(multiply(sk_c7,sk_c7),sk_c8)**.
% 0.19/0.43 156[5:Rew:105.0,151.0] || -> equal(identity,sk_c6)**.
% 0.19/0.43 157[5:Rew:156.0,32.0] || -> equal(multiply(sk_c6,u),u)**.
% 0.19/0.43 158[5:Rew:156.0,33.0] || -> equal(multiply(inverse(u),u),sk_c6)**.
% 0.19/0.43 159[5:Rew:156.0,105.0] || -> equal(multiply(sk_c7,sk_c8),sk_c6)**.
% 0.19/0.43 160[5:Rew:156.0,107.0] || -> equal(multiply(sk_c8,sk_c4),sk_c6)**.
% 0.19/0.43 161[5:Rew:156.0,141.0] || -> equal(multiply(sk_c7,sk_c6),sk_c4)**.
% 0.19/0.43 162[5:Rew:156.0,95.0] || equal(inverse(sk_c6),sk_c8) equal(sk_c8,u) equal(multiply(sk_c8,u),sk_c7)** -> .
% 0.19/0.43 163[7:Rew:132.0,152.0] || -> equal(sk_c8,sk_c6)**.
% 0.19/0.43 164[7:Rew:163.0,90.0] || -> equal(inverse(sk_c6),sk_c7)**.
% 0.19/0.43 165[7:Rew:163.0,100.0] || -> equal(inverse(sk_c4),sk_c6)**.
% 0.19/0.43 171[6:Rew:157.0,146.0] || -> equal(multiply(sk_c7,multiply(sk_c7,u)),u)**.
% 0.19/0.43 173[7:Rew:157.0,160.0,163.0,160.0] || -> equal(sk_c6,sk_c4)**.
% 0.19/0.43 176[7:Rew:173.0,163.0] || -> equal(sk_c8,sk_c4)**.
% 0.19/0.43 177[7:Rew:173.0,164.0] || -> equal(inverse(sk_c4),sk_c7)**.
% 0.19/0.43 178[7:Rew:173.0,165.0] || -> equal(inverse(sk_c4),sk_c4)**.
% 0.19/0.43 179[7:Rew:173.0,157.0] || -> equal(multiply(sk_c4,u),u)**.
% 0.19/0.43 181[7:Rew:177.0,178.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.43 184[7:Rew:181.0,173.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.43 186[7:Rew:181.0,176.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.43 187[7:Rew:181.0,177.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.43 191[7:Rew:181.0,179.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.43 192[7:Rew:184.0,158.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.19/0.43 200[7:Rew:191.0,162.2,186.0,162.2,186.0,162.1,187.0,162.0,184.0,162.0,186.0,162.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.43 201[7:Obv:200.1] || equal(u,sk_c7)* -> .
% 0.19/0.43 202[7:UnC:201.0,192.0] || -> .
% 0.19/0.43 204[7:Spt:202.0,3.1,110.0] || equal(multiply(sk_c4,sk_c7),sk_c8)** -> .
% 0.19/0.43 205[7:Spt:202.0,3.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.43 206[7:Rew:150.0,204.0] || equal(multiply(sk_c7,sk_c7),sk_c8)** -> .
% 0.19/0.43 207[7:Rew:132.0,206.0] || equal(sk_c8,sk_c6)** -> .
% 0.19/0.43 208[6:Rew:132.0,27.1,150.0,27.1] || -> equal(inverse(sk_c2),sk_c8)** equal(sk_c8,sk_c6).
% 0.19/0.43 209[7:MRR:208.1,207.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.43 210[6:Rew:157.0,119.0] || -> equal(multiply(sk_c8,u),multiply(sk_c7,u))**.
% 0.19/0.43 214[6:Rew:210.0,108.0] || -> equal(multiply(sk_c7,sk_c6),sk_c7)**.
% 0.19/0.43 215[6:Rew:161.0,214.0] || -> equal(sk_c4,sk_c7)**.
% 0.19/0.43 222[6:Rew:132.0,9.0,215.0,9.0] || -> equal(sk_c8,sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.43 223[7:MRR:222.0,207.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.43 224[6:Rew:210.0,15.1,132.0,15.0,215.0,15.0] || -> equal(sk_c8,sk_c6) equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.43 225[7:MRR:224.0,207.0] || -> equal(multiply(sk_c7,sk_c3),sk_c7)**.
% 0.19/0.43 226[6:Rew:132.0,21.0,215.0,21.0] || -> equal(sk_c8,sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 227[7:MRR:226.0,207.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 259[7:SpR:205.0,158.0] || -> equal(multiply(sk_c8,sk_c1),sk_c6)**.
% 0.19/0.43 261[7:SpR:209.0,158.0] || -> equal(multiply(sk_c8,sk_c2),sk_c6)**.
% 0.19/0.43 263[7:Rew:210.0,259.0] || -> equal(multiply(sk_c7,sk_c1),sk_c6)**.
% 0.19/0.43 264[7:Rew:210.0,261.0] || -> equal(multiply(sk_c7,sk_c2),sk_c6)**.
% 0.19/0.43 274[0:SpR:122.0,122.0] || -> equal(multiply(inverse(inverse(u)),v),multiply(u,v))**.
% 0.19/0.43 277[7:SpR:223.0,122.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.19/0.43 284[7:SpR:227.0,122.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.43 286[5:SpR:158.0,122.0] || -> equal(multiply(inverse(inverse(u)),sk_c6),u)**.
% 0.19/0.43 291[7:Rew:205.0,277.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.43 292[7:Rew:210.0,291.0] || -> equal(multiply(sk_c7,sk_c8),sk_c7)**.
% 0.19/0.43 293[7:Rew:159.0,292.0] || -> equal(sk_c6,sk_c7)**.
% 0.19/0.43 295[7:Rew:293.0,207.0] || equal(sk_c8,sk_c7)** -> .
% 0.19/0.43 299[7:Rew:293.0,157.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.43 301[7:Rew:293.0,263.0] || -> equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.19/0.43 302[7:Rew:293.0,264.0] || -> equal(multiply(sk_c7,sk_c2),sk_c7)**.
% 0.19/0.43 304[7:Rew:299.0,225.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.43 305[7:Rew:299.0,171.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.43 306[7:Rew:299.0,210.0] || -> equal(multiply(sk_c8,u),u)**.
% 0.19/0.43 317[7:Rew:299.0,301.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.43 325[7:Rew:317.0,295.0] || equal(sk_c8,sk_c1)** -> .
% 0.19/0.43 327[7:Rew:317.0,304.0] || -> equal(sk_c3,sk_c1)**.
% 0.19/0.43 328[7:Rew:317.0,302.0] || -> equal(multiply(sk_c1,sk_c2),sk_c1)**.
% 0.19/0.43 329[7:Rew:317.0,305.0] || -> equal(multiply(sk_c1,u),u)**.
% 0.19/0.43 330[7:Rew:329.0,328.0] || -> equal(sk_c2,sk_c1)**.
% 0.19/0.43 351[7:Rew:330.0,284.0,327.0,284.0] || -> equal(multiply(inverse(sk_c1),sk_c1),sk_c8)**.
% 0.19/0.43 352[7:Rew:205.0,351.0] || -> equal(multiply(sk_c8,sk_c1),sk_c8)**.
% 0.19/0.43 353[7:Rew:306.0,352.0] || -> equal(sk_c8,sk_c1)**.
% 0.19/0.43 354[7:MRR:353.0,325.0] || -> .
% 0.19/0.43 372[6:Spt:354.0,4.1,108.0] || equal(multiply(sk_c8,sk_c6),sk_c7)** -> .
% 0.19/0.43 373[6:Spt:354.0,4.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.43 374[5:Rew:274.0,286.0] || -> equal(multiply(u,sk_c6),u)**.
% 0.19/0.43 375[6:Rew:374.0,372.0] || equal(sk_c8,sk_c7)** -> .
% 0.19/0.43 383[5:Rew:374.0,28.1] || -> equal(inverse(sk_c2),sk_c8)** equal(sk_c8,sk_c7).
% 0.19/0.43 384[6:MRR:383.1,375.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.43 392[5:Rew:374.0,16.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 393[6:MRR:392.0,375.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 394[5:Rew:374.0,22.0] || -> equal(sk_c8,sk_c7) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 395[6:MRR:394.0,375.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 426[6:SpR:395.0,122.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.43 428[6:Rew:393.0,426.0,384.0,426.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.43 429[6:MRR:428.0,375.0] || -> .
% 0.19/0.43 430[5:Spt:429.0,5.1,102.0] || equal(multiply(sk_c5,sk_c8),sk_c6)** -> .
% 0.19/0.43 431[5:Spt:429.0,5.0] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.43 432[5:Rew:135.0,430.0] || equal(multiply(sk_c4,sk_c8),sk_c6)** -> .
% 0.19/0.43 433[5:Rew:150.0,432.0] || equal(multiply(sk_c7,sk_c8),sk_c6)** -> .
% 0.19/0.43 434[5:Rew:105.0,433.0] || equal(identity,sk_c6)** -> .
% 0.19/0.43 435[4:Rew:105.0,29.1,150.0,29.1,135.0,29.1] || -> equal(inverse(sk_c2),sk_c8)** equal(identity,sk_c6).
% 0.19/0.43 436[5:MRR:435.1,434.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.43 437[4:Rew:105.0,11.0,150.0,11.0,135.0,11.0] || -> equal(identity,sk_c6) equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.43 438[5:MRR:437.0,434.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.43 439[4:Rew:105.0,17.0,150.0,17.0,135.0,17.0] || -> equal(identity,sk_c6) equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 440[5:MRR:439.0,434.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 441[4:Rew:105.0,23.0,150.0,23.0,135.0,23.0] || -> equal(identity,sk_c6) equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 442[5:MRR:441.0,434.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 465[5:SpR:438.0,122.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.19/0.43 467[5:Rew:431.0,465.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.43 469[5:SpR:440.0,122.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.19/0.43 471[5:Rew:90.0,469.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.43 473[5:SpR:442.0,122.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.43 475[5:Rew:440.0,473.0,436.0,473.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.43 476[5:Rew:475.0,90.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.43 481[5:Rew:475.0,105.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.43 486[5:Rew:475.0,95.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.43 494[5:Rew:475.0,467.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.43 497[5:Rew:471.0,481.0] || -> equal(identity,sk_c3)**.
% 0.19/0.43 500[5:Rew:497.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.43 503[5:Rew:471.0,494.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.43 505[5:Rew:503.0,497.0] || -> equal(identity,sk_c7)**.
% 0.19/0.43 511[5:Rew:503.0,500.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.43 528[5:Rew:511.0,486.2,475.0,486.1,476.0,486.0,505.0,486.0,475.0,486.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.43 529[5:Obv:528.1] || equal(u,sk_c7)* -> .
% 0.19/0.43 530[5:UnC:529.0,122.0] || -> .
% 0.19/0.43 532[4:Spt:530.0,2.0,100.0] || equal(inverse(sk_c4),sk_c8)** -> .
% 0.19/0.43 533[4:Spt:530.0,2.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.43 534[4:MRR:26.0,532.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.43 535[4:MRR:8.0,532.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.43 536[4:MRR:14.0,532.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.43 537[4:MRR:20.0,532.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.43 561[4:SpR:535.0,122.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.19/0.43 563[4:Rew:533.0,561.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.43 565[4:SpR:536.0,122.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.19/0.43 567[4:Rew:90.0,565.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.43 569[4:SpR:537.0,122.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.43 571[4:Rew:536.0,569.0,534.0,569.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.43 573[4:Rew:571.0,90.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.43 576[4:Rew:571.0,105.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.43 584[4:Rew:571.0,95.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.43 591[4:Rew:571.0,563.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.43 594[4:Rew:567.0,576.0] || -> equal(identity,sk_c3)**.
% 0.19/0.43 596[4:Rew:594.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.43 599[4:Rew:567.0,591.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.43 601[4:Rew:599.0,594.0] || -> equal(identity,sk_c7)**.
% 0.19/0.43 607[4:Rew:599.0,596.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.43 623[4:Rew:607.0,584.2,571.0,584.1,573.0,584.0,601.0,584.0,571.0,584.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.43 624[4:Obv:623.1] || equal(u,sk_c7)* -> .
% 0.19/0.44 625[4:UnC:624.0,122.0] || -> .
% 0.19/0.44 627[3:Spt:625.0,6.0,98.0] || equal(inverse(sk_c5),sk_c8)** -> .
% 0.19/0.44 628[3:Spt:625.0,6.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.44 629[3:MRR:30.0,627.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.44 630[3:MRR:12.0,627.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.44 631[3:MRR:18.0,627.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.44 632[3:MRR:24.0,627.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.44 644[3:SpR:630.0,122.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.19/0.44 646[3:Rew:628.0,644.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.44 648[3:SpR:631.0,122.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.19/0.44 650[3:Rew:90.0,648.0] || -> equal(multiply(sk_c7,sk_c7),sk_c3)**.
% 0.19/0.44 652[3:SpR:632.0,122.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.44 654[3:Rew:631.0,652.0,629.0,652.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.44 656[3:Rew:654.0,90.0] || -> equal(inverse(sk_c7),sk_c7)**.
% 0.19/0.44 659[3:Rew:654.0,105.0] || -> equal(multiply(sk_c7,sk_c7),identity)**.
% 0.19/0.44 665[3:Rew:654.0,95.2] || equal(inverse(identity),sk_c8) equal(sk_c8,u) equal(multiply(sk_c7,u),sk_c7)** -> .
% 0.19/0.44 671[3:Rew:654.0,646.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.44 673[3:Rew:650.0,659.0] || -> equal(identity,sk_c3)**.
% 0.19/0.44 674[3:Rew:673.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.44 676[3:Rew:650.0,671.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.44 678[3:Rew:676.0,673.0] || -> equal(identity,sk_c7)**.
% 0.19/0.44 681[3:Rew:676.0,674.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.44 690[3:Rew:681.0,665.2,654.0,665.1,656.0,665.0,678.0,665.0,654.0,665.0] || equal(sk_c7,sk_c7)* equal(sk_c7,u)* equal(u,sk_c7)* -> .
% 0.19/0.44 691[3:Obv:690.1] || equal(u,sk_c7)* -> .
% 0.19/0.44 692[3:UnC:691.0,122.0] || -> .
% 0.19/0.44 694[2:Spt:692.0,1.0,90.0] || equal(inverse(sk_c8),sk_c7)** -> .
% 0.19/0.44 695[2:Spt:692.0,1.1] || -> equal(inverse(sk_c1),sk_c8)**.
% 0.19/0.44 696[2:MRR:25.0,694.0] || -> equal(inverse(sk_c2),sk_c8)**.
% 0.19/0.44 697[2:MRR:7.0,694.0] || -> equal(multiply(sk_c1,sk_c7),sk_c8)**.
% 0.19/0.44 698[2:MRR:13.0,694.0] || -> equal(multiply(sk_c8,sk_c3),sk_c7)**.
% 0.19/0.44 699[2:MRR:19.0,694.0] || -> equal(multiply(sk_c2,sk_c8),sk_c3)**.
% 0.19/0.44 705[2:SpR:697.0,122.0] || -> equal(multiply(inverse(sk_c1),sk_c8),sk_c7)**.
% 0.19/0.44 707[2:Rew:695.0,705.0] || -> equal(multiply(sk_c8,sk_c8),sk_c7)**.
% 0.19/0.44 709[2:SpR:698.0,122.0] || -> equal(multiply(inverse(sk_c8),sk_c7),sk_c3)**.
% 0.19/0.44 712[2:SpR:699.0,122.0] || -> equal(multiply(inverse(sk_c2),sk_c3),sk_c8)**.
% 0.19/0.44 714[2:Rew:698.0,712.0,696.0,712.0] || -> equal(sk_c8,sk_c7)**.
% 0.19/0.44 715[2:Rew:714.0,695.0] || -> equal(inverse(sk_c1),sk_c7)**.
% 0.19/0.44 717[2:Rew:714.0,694.0] || equal(inverse(sk_c7),sk_c7)** -> .
% 0.19/0.44 723[2:Rew:714.0,707.0] || -> equal(multiply(sk_c7,sk_c7),sk_c7)**.
% 0.19/0.44 725[2:Rew:714.0,709.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c3)**.
% 0.19/0.44 727[2:Rew:33.0,725.0] || -> equal(identity,sk_c3)**.
% 0.19/0.44 728[2:Rew:727.0,32.0] || -> equal(multiply(sk_c3,u),u)**.
% 0.19/0.44 729[2:Rew:727.0,33.0] || -> equal(multiply(inverse(u),u),sk_c3)**.
% 0.19/0.44 752[2:SpR:723.0,122.0] || -> equal(multiply(inverse(sk_c7),sk_c7),sk_c7)**.
% 0.19/0.44 754[2:Rew:729.0,752.0] || -> equal(sk_c3,sk_c7)**.
% 0.19/0.44 758[2:Rew:754.0,728.0] || -> equal(multiply(sk_c7,u),u)**.
% 0.19/0.44 759[2:Rew:754.0,729.0] || -> equal(multiply(inverse(u),u),sk_c7)**.
% 0.19/0.44 781[2:SpR:715.0,759.0] || -> equal(multiply(sk_c7,sk_c1),sk_c7)**.
% 0.19/0.44 786[2:Rew:758.0,781.0] || -> equal(sk_c7,sk_c1)**.
% 0.19/0.44 788[2:Rew:786.0,715.0] || -> equal(inverse(sk_c1),sk_c1)**.
% 0.19/0.44 789[2:Rew:786.0,717.0] || equal(inverse(sk_c1),sk_c1)** -> .
% 0.19/0.44 797[2:Rew:788.0,789.0] || equal(sk_c1,sk_c1)* -> .
% 0.19/0.44 798[2:Obv:797.0] || -> .
% 0.19/0.44 % SZS output end Refutation
% 0.19/0.44 Formulae used in the proof : prove_this_1 prove_this_2 prove_this_3 prove_this_4 prove_this_5 prove_this_6 prove_this_7 prove_this_8 prove_this_9 prove_this_11 prove_this_12 prove_this_13 prove_this_14 prove_this_15 prove_this_16 prove_this_17 prove_this_18 prove_this_19 prove_this_20 prove_this_21 prove_this_22 prove_this_23 prove_this_24 prove_this_25 prove_this_26 prove_this_27 prove_this_28 prove_this_29 prove_this_30 prove_this_31 left_identity left_inverse associativity
% 0.19/0.44
%------------------------------------------------------------------------------